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Today’s Gambling Myth: The Monte Carlo Fallacy

Posted by in Gaming, Las Vegas Casinos. 1 Comment on Today’s Gambling Myth: The Monte Carlo Fallacy.

It’s called a number of things. The “gambler’s fallacy,” and the “Monte Carlo fallacy,” and even “the fallacy of the maturity of chances.” We like that last one because it makes this blog sound smarter than it really is.

But it all boils down to one basic, misguided belief: In games of chance, like roulette or craps, if a certain outcome hasn’t happened in awhile, it’s more likely to occur in the future.

Seriously, black has hit, like, six times in a row. Has to be red next. Definitely.

roulette numbers

We knew that was going to happen. It had to. Probably.

But here’s why it’s a myth. Every roll of the dice, and every spin at roulette, is its own thing. You’ve probably even heard the expression, “The dice have no memory.” As in life, just because something has happened a lot in the past doesn’t mean it’s more or less likely to happen in the future. There’s really no such thing as a certain outcome being “overdue.” The odds remain the same, no matter what’s transpired during a previous roll or spin. And not surprisingly, those odds always favor the house.

More than a few players have been stung by the Monte Carlo fallacy. (It’s called that because one of the most famous examples of this concept took place at a Monte Carlo casino in 1913. Monte Carlo is in Monaco, and it’s a lot like Las Vegas, just yawnier.)

Think your number or color has to hit soon? The longest recorded streak of one color in roulette in American casino history happened in 1943 when the color red won 32 consecutive times. In a row. The people convinced black had to hit next were absolutely right. Eventually.

roulette numbers

We know what you're up to, illusion of predictability.

Does knowing about the gambler’s fallacy mean you can’t play your hunches or try to outguess your favorite game? Of course not. People win fortunes because of lucky streaks that defy the odds (just ask the woman who had a craps roll for four hours and 18 minutes at Borgata in Atlantic City). But do yourself a favor and know the odds you’re up against (they vary greatly depending upon the game), and don’t fall into the “double up to catch up” trap. As they say in the financial world: “Past performance is not a guarantee of future results.”

You can read more about the gambler’s fallacy on Wikipedia and

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  1. Matthew

    It is true that these outcomes are independent of each other. With that said, it is possible in theory to devise a betting strategy that beats the house with probability=1. Playing the strategy: Bet x if won the last time else bet x*(2^n) if lost n times before wins in the limit as n –> infinity. The strategy is an ex-ante bet that there will not be an infinite series of the same outcome, which is true with probability=1.

    This is not a practical strategy because houses have both minimums and maximums which both constrain the size of “n”, define this constrained size to be N. With this said, you could easily calculate the probability of having a series of N outcomes to be (1-p^N)/(1-p) where p is the probability of losing.

    Note that this does not calculate the Expected Value of playing this strategy, which in a finite space should be negative. However, the negative Expected Value is driven by the size of the last bet if you lose N consecutive games. Note that the size of the bet is growing exponentially by 2^n. Thus we should be able to say that the probability of a negative expected value is (1-p^N)/(1-p) although I must admit that I am too lazy to prove this at the moment :)

    Bottom line, it does not seem possible to escape a game of negative expectations in a finite space but the probability of a large negative loss might not be that high depending on the limits that the house puts on you. However, do not come crying to me if you lose your life savings in a high stakes game because I warned you that gambling is indeed a game of negative expectations (expect to lose is the only rational expectation).